Re: [sympy] hyint: hybrid (symbolic-numeric) integration
> I like the idea of using some faster linear algebra as a preprocessor > to reduce the size of the problem to be solved. You could then take > the reduced problem and solve it with exact symbolic arithmetic. The > worst that can happen is you might drop an ansatz that shouldn't have > been dropped, but you would still always give a symbolically correct > answer when you do. I'm testing this idea and it seems to be working fine. I just uploaded a new version of hyint that exports a `hints(eq, x)` function to return a filtered list of ansatz for eq. This version accepts expressions with symbolic constants. The output of hyint.hints() can then be fed to the `hints` argument of heurisch as a preprocessor. Example: >>> from sympy import log >>> from sympy.integrals.heurisch import heurisch >>> from sympy.abc import a, x >>> import hyint >>> y = log(log(x) + a) / x >>> heurisch(y, x) # returns None, no solution >>> hints = hyint.hints(y, x) >>> print(hints) [log(a + log(x)), log(x)*log(a + log(x)), log(x)] >>> heurisch(y, x, hints=hints) a*log(a + log(x)) + log(x)*log(a + log(x)) - log(x) Thanks, Shahriar Iravanian On Friday, September 1, 2023 at 3:58:27 PM UTC-4 asme...@gmail.com wrote: > On Fri, Sep 1, 2023 at 4:12 AM Oscar Benjamin > wrote: > > > > On Fri, 1 Sept 2023 at 06:45, Aaron Meurer wrote: > > > > > > I like the idea of using some faster linear algebra as a preprocessor > > > to reduce the size of the problem to be solved. You could then take > > > the reduced problem and solve it with exact symbolic arithmetic. The > > > worst that can happen is you might drop an ansatz that shouldn't have > > > been dropped, but you would still always give a symbolically correct > > > answer when you do. > > > > > > If heurisch could support much larger, possibly linearly dependent > > > ansatz, then that would open up a lot of possibilities, like for > > > instance, trying to use ansatz coming from both sqrt(x) and x/sqrt(x) > > > simultaneously. But right now it's way too slow even with just the > > > linear system it generates. > > > > I'm not sure if I've interpreted this point correctly but when > > heurisch is slow it is not usually because of the linear algebra part. > > Probably that is the easiest part to speed up as well. > > Maybe things have changed since the introduction of things like > DomainMatrix, but when I benchmarked it years ago this was the case. > That and the fact that it was using the dense poly representation with > hundreds of variables. > > > > > The slow parts of heurisch are converting back and forth between Expr > > and the domains, differentiation, and cancel. > > > > If heurisch was being rewritten then I think it could be written > > without the back and forth conversions. The differentiation could be > > handled in the domain representation. The cancellation could be > > handled there as well. > > We could probably merge a lot of the code in risch and heurisch, but > loosening the restrictive rigorous code from risch. Actually Risch > itself can solve some algebraic integrals if the restrictions are > removed (just the nonelementary integral errors would be incorrect). > > > > > I suspect that heurisch was implemented at a time when SymPy did not > > have as many of the pieces that it now has that you would want to use > > to implement the algorithm within the algebra subsystem rather than > > the symbolic subsystem. > > Yes, heurisch predates the polys module. I integrated it with the > polys back in 2012 or 2013, but I didn't really refactor it in any > major way. > > Aaron Meurer > > > > > Possibly the limiting factor for SymPy implementing heurisch in the > > ideal way right now is support for symbolic algebraic extensions like > > Q(x)[sqrt(x)] within the domain system although polys.agca has > > FiniteMonogenicExtension that could represent that. > > > > -- > > Oscar > > > > -- > > You received this message because you are subscribed to the Google > Groups "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to sympy+un...@googlegroups.com. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxSN%2BVBubjX6i3mq%3DwE7nXZSorg7drnSP_X3-2daxbzE0Q%40mail.gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/0025efdb-0dc4-4be0-8897-85c0ea2b50efn%40googlegroups.com.
Re: [sympy] hyint: hybrid (symbolic-numeric) integration
> This is a big problem for algebraic functions because they can be > represented in multiple different ways, and that representation can > affect the result of integration (a big piece of the "real" Risch > algorithm for algebraic functions is normalizing things so that this > isn't a problem). For example, the derivative of s = sqrt(x) can be > represented as 1/(2*s) or s/(2*x). The strength of the numerical method is that the distinction between 1/(2*s) and s/(2*x) is lost. We can have both expressions in the ansatz list, and one will be dropped because they are linearly dependent. > I like the idea of using some faster linear algebra as a preprocessor > to reduce the size of the problem to be solved. You could then take > the reduced problem and solve it with exact symbolic arithmetic. The > worst that can happen is you might drop an ansatz that shouldn't have > been dropped, but you would still always give a symbolically correct > answer when you do. This is the plan. We can use hyint to prune the set of ansatzes to those actually in the integral and then solve symbolically for the coefficients. > I'm also wondering if you've thought about symbolic constants and if > there's any tricks you could do to support them. I think there might > be, especially when still thinking about things in terms of just using > faster linear algebra as a pre-processor to a symbolic solve. The basic idea is to generate ansatzes with intact symbolic constants, but then substitute them with random numbers (same as we do for x), solve the integral with sparse regression, and then, starting with the pruned set of symbolic ansatzes, solve for the coefficients as above. Regarding improving the speed of calculations, I cannot comment on sympy linear solvers and polys module but should mention that symbolic-numeric methods can also improve the speed. Currently, hyint separates the symbolic part (ansatz generation) from the numerical part. But it is possible to mix numerical methods in ansatz generation. We can calculate only the diff of factors of the integrands and not the whole expressions. Afterward, ansatz generation can proceed mainly numerically (while keeping track of the path for each ansatz; polys may be helpful here). Finally, we can reconstruct the relevant ansatz symbolically. This way, we can skip most of the symbolic diffs and cancellations. Thanks, Shahriar Iravanian On Friday, September 1, 2023 at 3:58:27 PM UTC-4 asme...@gmail.com wrote: > On Fri, Sep 1, 2023 at 4:12 AM Oscar Benjamin > wrote: > > > > On Fri, 1 Sept 2023 at 06:45, Aaron Meurer wrote: > > > > > > I like the idea of using some faster linear algebra as a preprocessor > > > to reduce the size of the problem to be solved. You could then take > > > the reduced problem and solve it with exact symbolic arithmetic. The > > > worst that can happen is you might drop an ansatz that shouldn't have > > > been dropped, but you would still always give a symbolically correct > > > answer when you do. > > > > > > If heurisch could support much larger, possibly linearly dependent > > > ansatz, then that would open up a lot of possibilities, like for > > > instance, trying to use ansatz coming from both sqrt(x) and x/sqrt(x) > > > simultaneously. But right now it's way too slow even with just the > > > linear system it generates. > > > > I'm not sure if I've interpreted this point correctly but when > > heurisch is slow it is not usually because of the linear algebra part. > > Probably that is the easiest part to speed up as well. > > Maybe things have changed since the introduction of things like > DomainMatrix, but when I benchmarked it years ago this was the case. > That and the fact that it was using the dense poly representation with > hundreds of variables. > > > > > The slow parts of heurisch are converting back and forth between Expr > > and the domains, differentiation, and cancel. > > > > If heurisch was being rewritten then I think it could be written > > without the back and forth conversions. The differentiation could be > > handled in the domain representation. The cancellation could be > > handled there as well. > > We could probably merge a lot of the code in risch and heurisch, but > loosening the restrictive rigorous code from risch. Actually Risch > itself can solve some algebraic integrals if the restrictions are > removed (just the nonelementary integral errors would be incorrect). > > > > > I suspect that heurisch was implemented at a time when SymPy did not > > have as many of the pieces that it now has that you would want to use > > to implement the algorithm within the algebra subsystem rather than > > the symbolic subsystem. > > Yes, heurisch predates the polys module. I integrated it with the > polys back in 2012 or 2013, but I didn't really refactor it in any > major way. > > Aaron Meurer > > > > > Possibly the limiting factor for SymPy implementing heurisch in the > > ideal way right now is support for
Re: [sympy] hyint: hybrid (symbolic-numeric) integration
On Fri, Sep 1, 2023 at 4:12 AM Oscar Benjamin wrote: > > On Fri, 1 Sept 2023 at 06:45, Aaron Meurer wrote: > > > > I like the idea of using some faster linear algebra as a preprocessor > > to reduce the size of the problem to be solved. You could then take > > the reduced problem and solve it with exact symbolic arithmetic. The > > worst that can happen is you might drop an ansatz that shouldn't have > > been dropped, but you would still always give a symbolically correct > > answer when you do. > > > > If heurisch could support much larger, possibly linearly dependent > > ansatz, then that would open up a lot of possibilities, like for > > instance, trying to use ansatz coming from both sqrt(x) and x/sqrt(x) > > simultaneously. But right now it's way too slow even with just the > > linear system it generates. > > I'm not sure if I've interpreted this point correctly but when > heurisch is slow it is not usually because of the linear algebra part. > Probably that is the easiest part to speed up as well. Maybe things have changed since the introduction of things like DomainMatrix, but when I benchmarked it years ago this was the case. That and the fact that it was using the dense poly representation with hundreds of variables. > > The slow parts of heurisch are converting back and forth between Expr > and the domains, differentiation, and cancel. > > If heurisch was being rewritten then I think it could be written > without the back and forth conversions. The differentiation could be > handled in the domain representation. The cancellation could be > handled there as well. We could probably merge a lot of the code in risch and heurisch, but loosening the restrictive rigorous code from risch. Actually Risch itself can solve some algebraic integrals if the restrictions are removed (just the nonelementary integral errors would be incorrect). > > I suspect that heurisch was implemented at a time when SymPy did not > have as many of the pieces that it now has that you would want to use > to implement the algorithm within the algebra subsystem rather than > the symbolic subsystem. Yes, heurisch predates the polys module. I integrated it with the polys back in 2012 or 2013, but I didn't really refactor it in any major way. Aaron Meurer > > Possibly the limiting factor for SymPy implementing heurisch in the > ideal way right now is support for symbolic algebraic extensions like > Q(x)[sqrt(x)] within the domain system although polys.agca has > FiniteMonogenicExtension that could represent that. > > -- > Oscar > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxSN%2BVBubjX6i3mq%3DwE7nXZSorg7drnSP_X3-2daxbzE0Q%40mail.gmail.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6JmY0mA_bfTKggY_%3DtTR74j%2BQ0MkViPeeCs35-yOQihkg%40mail.gmail.com.
Re: [sympy] hyint: hybrid (symbolic-numeric) integration
On Fri, 1 Sept 2023 at 06:45, Aaron Meurer wrote: > > I like the idea of using some faster linear algebra as a preprocessor > to reduce the size of the problem to be solved. You could then take > the reduced problem and solve it with exact symbolic arithmetic. The > worst that can happen is you might drop an ansatz that shouldn't have > been dropped, but you would still always give a symbolically correct > answer when you do. > > If heurisch could support much larger, possibly linearly dependent > ansatz, then that would open up a lot of possibilities, like for > instance, trying to use ansatz coming from both sqrt(x) and x/sqrt(x) > simultaneously. But right now it's way too slow even with just the > linear system it generates. I'm not sure if I've interpreted this point correctly but when heurisch is slow it is not usually because of the linear algebra part. Probably that is the easiest part to speed up as well. The slow parts of heurisch are converting back and forth between Expr and the domains, differentiation, and cancel. If heurisch was being rewritten then I think it could be written without the back and forth conversions. The differentiation could be handled in the domain representation. The cancellation could be handled there as well. I suspect that heurisch was implemented at a time when SymPy did not have as many of the pieces that it now has that you would want to use to implement the algorithm within the algebra subsystem rather than the symbolic subsystem. Possibly the limiting factor for SymPy implementing heurisch in the ideal way right now is support for symbolic algebraic extensions like Q(x)[sqrt(x)] within the domain system although polys.agca has FiniteMonogenicExtension that could represent that. -- Oscar -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHVvXxSN%2BVBubjX6i3mq%3DwE7nXZSorg7drnSP_X3-2daxbzE0Q%40mail.gmail.com.
Re: [sympy] hyint: hybrid (symbolic-numeric) integration
On Thu, Aug 31, 2023 at 8:22 PM Shahriar Iravanian wrote: > > Thank you very much for your comments. > > While hyint ansatz generation is similar in spirit to heurisch, it is less > rigorous and more > heuristic. One reason is that the numerical portion of hyint is much more > forgiving and > can filter out many undesirable ansatzes (by using QR decomposition to remove > linearly > dependent ones and sparse regression to solve the integral). Therefore, we > can generate > many different forms of ansatz, which allows hyint to solve integrals beyond > what > heurisch can do. > > For example, I use a set of 170 test cases (listed in test.py) to test hyint. > The current version > can solve 154 of them; heurisch solves 126 (of course, this list is curated > for hyint). > > Some integrals that hyint can solve and heurisch cannot: > > x/sqrt(x - 1) => 2*x*sqrt(x - 1)/3 + 4*sqrt(x - 1)/3 > 1/sqrt(x**2 + 4) => asinh(x/2) > sqrt(x)*log(x) => 2*x**(3/2)*log(x)/3 - 4*x**(3/2)/9 > log(log(x))/x => log(x)*log(log(x)) - log(x) > log(cos(x))*tan(x) => -log(cos(x))**2/2 > sin(x + 1)/(x + 1) => Si(x + 1) > sqrt(1 - sin(x)) => 2*cos(x)/sqrt(1 - sin(x)) By the way, a big problem with heurisch is that it's very sensitive to the way the derivative of the expression is represented, since that's how it generates the ansatz. This is fundamental to the approach, but an issue is that it just directly uses whatever sympy.diff() returns. This is a big problem for algebraic functions because they can be represented in multiple different ways, and that representation can affect the result of integration (a big piece of the "real" Risch algorithm for algebraic functions is normalizing things so that this isn't a problem). For example, the derivative of s = sqrt(x) can be represented as 1/(2*s) or s/(2*x). SymPy happens to use the former form, because of the way the core combines exponents, but there are integrals with square roots where heurisch can't find the answer but would if it used the latter form (not so much because the latter form is better, although in some ways it is since it's a polynomial in s, but usually just by dumb luck of the way it generates the ansatz). > > Some integrals that heurisch can solve and hyint cannot: > > exp(x)/(exp(2*x) - 1) => log(exp(x) - 1)/2 - log(exp(x) + 1)/2 > tan(x)**3 => -log(tan(x)**2 + 1)/2 + tan(x)**2/2 > > > Actually it wouldn't be much work to generalize this to something that > > gives an exact answer at least some of the time. > > I completely agree. I believe the main application of hyint is as an ansatz > discovery > engine rather than a standalone integrator. This is a line of research I'm > actively > pursuing and would appreciate help, comments, and collaboration! I like the idea of using some faster linear algebra as a preprocessor to reduce the size of the problem to be solved. You could then take the reduced problem and solve it with exact symbolic arithmetic. The worst that can happen is you might drop an ansatz that shouldn't have been dropped, but you would still always give a symbolically correct answer when you do. If heurisch could support much larger, possibly linearly dependent ansatz, then that would open up a lot of possibilities, like for instance, trying to use ansatz coming from both sqrt(x) and x/sqrt(x) simultaneously. But right now it's way too slow even with just the linear system it generates. I'm also wondering if you've thought about symbolic constants and if there's any tricks you could do to support them. I think there might be, especially when still thinking about things in terms of just using faster linear algebra as a pre-processor to a symbolic solve. Aaron Meurer > > -- Shahriar > > On Thursday, August 31, 2023 at 6:48:24 PM UTC-4 asme...@gmail.com wrote: >> >> On Thu, Aug 31, 2023 at 5:07 AM Oscar Benjamin >> wrote: >> > >> > On Tue, 29 Aug 2023 at 07:09, Shahriar Iravanian >> > wrote: >> > > >> > > Hi All, >> > > >> > >> > Hi Shahriar, >> > >> > > I have uploaded a new package, hyint, to github and PyPi. It is a hybrid >> > > (symbolic-numeric) integration package on top of SymPy and numpy/scipy. >> > > I would appreciate it if it is added to the list of projects using SymPy. >> > > >> > > You can find it at https://github.com/siravan/hyint or install it as >> > > 'pip install hyint'. >> > > >> > > hyint uses an ansatz generation algorithm similar to the Risch-Bronstein >> > > poor man's integrator combined with a sparse regression algorithm >> > > adopted from the Sparse identification of nonlinear dynamics (SINDy) to >> > > solve indefinite integration problems to univariate expressions. It can >> > > solve a large subset of standard elementary integrals despite a very >> > > small size (a few hundred lines of code). >> > > >> > > I'm one of the principal contributors to SymbolicNumericIntegartion.jl >> > > (https://github.com/SciML/SymbolicNumericIntegration.jl), which is a >> > > Julia package for symbolic-numeric
Re: [sympy] hyint: hybrid (symbolic-numeric) integration
Thank you very much for your comments. While hyint ansatz generation is similar in spirit to heurisch, it is less rigorous and more heuristic. One reason is that the numerical portion of hyint is much more forgiving and can filter out many undesirable ansatzes (by using QR decomposition to remove linearly dependent ones and sparse regression to solve the integral). Therefore, we can generate many different forms of ansatz, which allows hyint to solve integrals beyond what heurisch can do. For example, I use a set of 170 test cases (listed in test.py) to test hyint. The current version can solve 154 of them; heurisch solves 126 (of course, this list is curated for hyint). Some integrals that hyint can solve and heurisch cannot: x/sqrt(x - 1) => 2*x*sqrt(x - 1)/3 + 4*sqrt(x - 1)/3 1/sqrt(x**2 + 4) => asinh(x/2) sqrt(x)*log(x) => 2*x**(3/2)*log(x)/3 - 4*x**(3/2)/9 log(log(x))/x => log(x)*log(log(x)) - log(x) log(cos(x))*tan(x) => -log(cos(x))**2/2 sin(x + 1)/(x + 1) => Si(x + 1) sqrt(1 - sin(x)) => 2*cos(x)/sqrt(1 - sin(x)) Some integrals that heurisch can solve and hyint cannot: exp(x)/(exp(2*x) - 1) => log(exp(x) - 1)/2 - log(exp(x) + 1)/2 tan(x)**3 => -log(tan(x)**2 + 1)/2 + tan(x)**2/2 > Actually it wouldn't be much work to generalize this to something that > gives an exact answer at least some of the time. I completely agree. I believe the main application of hyint is as an ansatz discovery engine rather than a standalone integrator. This is a line of research I'm actively pursuing and would appreciate help, comments, and collaboration! -- Shahriar On Thursday, August 31, 2023 at 6:48:24 PM UTC-4 asme...@gmail.com wrote: > On Thu, Aug 31, 2023 at 5:07 AM Oscar Benjamin > wrote: > > > > On Tue, 29 Aug 2023 at 07:09, Shahriar Iravanian > wrote: > > > > > > Hi All, > > > > > > > Hi Shahriar, > > > > > I have uploaded a new package, hyint, to github and PyPi. It is a > hybrid (symbolic-numeric) integration package on top of SymPy and > numpy/scipy. I would appreciate it if it is added to the list of projects > using SymPy. > > > > > > You can find it at https://github.com/siravan/hyint or install it as > 'pip install hyint'. > > > > > > hyint uses an ansatz generation algorithm similar to the > Risch-Bronstein poor man's integrator combined with a sparse regression > algorithm > > > adopted from the Sparse identification of nonlinear dynamics (SINDy) > to solve indefinite integration problems to univariate expressions. It can > solve a large subset of standard elementary integrals despite a very small > size (a few hundred lines of code). > > > > > > I'm one of the principal contributors to SymbolicNumericIntegartion.jl > (https://github.com/SciML/SymbolicNumericIntegration.jl), which is a > Julia package for symbolic-numeric integration and is the basis of hyint. > > > > This sounds excellent. Yes, you can add it to the list of projects > > using SymPy using a pull request, I think to the website repo. > > > > How exactly is it different from Bronstein's poor man's integrator? > > > > SymPy has an integration algorithm called heurisch which is based on > > the poor man's integrator but uses exact rather than approximate > > solutions to the linear equations. Is exact vs approximate the main > > distinction here between what hyint does and what heurisch does? > > Judging from the examples, it looks like it > > In: hyint.integrate(1 / (x**3 - 2*x + 1), x) > Out: 2.17082039324994*log(x - 1) + 1.34164078649988*log(x + 1/2 + > sqrt(5)/2) - 1.17082039324993*log(x**3 - 2*x + 1) > > And looking at the code, I'd say a difference is that the Bronstein > algorithm is more rigorous and general in how it generates its ansatz. > But actually one of the reasons heurisch() is so slow is that it can > generate ansatz that are huge (especially when it's given an integrand > that doesn't have an answer to begin with). Employing some heuristics > like the ones used here in heurisch could help it out. > > Actually it wouldn't be much work to generalize this to something that > gives an exact answer at least some of the time. For example, you > could use nsimplify() to guess at exact values for numeric > coefficients. As long as diff(answer) - integrand symbolically > simplifies to 0 you know you have a correct answer. > > Aaron Meurer > > > > > -- > > Oscar > > > > -- > > You received this message because you are subscribed to the Google > Groups "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to sympy+un...@googlegroups.com. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxRyJ3FUZ1pN6GACMoHZBYGbUJAavKq5Y1RW5__1nFAT8w%40mail.gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the
Re: [sympy] hyint: hybrid (symbolic-numeric) integration
On Thu, Aug 31, 2023 at 5:07 AM Oscar Benjamin wrote: > > On Tue, 29 Aug 2023 at 07:09, Shahriar Iravanian > wrote: > > > > Hi All, > > > > Hi Shahriar, > > > I have uploaded a new package, hyint, to github and PyPi. It is a hybrid > > (symbolic-numeric) integration package on top of SymPy and numpy/scipy. I > > would appreciate it if it is added to the list of projects using SymPy. > > > > You can find it at https://github.com/siravan/hyint or install it as 'pip > > install hyint'. > > > > hyint uses an ansatz generation algorithm similar to the Risch-Bronstein > > poor man's integrator combined with a sparse regression algorithm > > adopted from the Sparse identification of nonlinear dynamics (SINDy) to > > solve indefinite integration problems to univariate expressions. It can > > solve a large subset of standard elementary integrals despite a very small > > size (a few hundred lines of code). > > > > I'm one of the principal contributors to SymbolicNumericIntegartion.jl > > (https://github.com/SciML/SymbolicNumericIntegration.jl), which is a Julia > > package for symbolic-numeric integration and is the basis of hyint. > > This sounds excellent. Yes, you can add it to the list of projects > using SymPy using a pull request, I think to the website repo. > > How exactly is it different from Bronstein's poor man's integrator? > > SymPy has an integration algorithm called heurisch which is based on > the poor man's integrator but uses exact rather than approximate > solutions to the linear equations. Is exact vs approximate the main > distinction here between what hyint does and what heurisch does? Judging from the examples, it looks like it In: hyint.integrate(1 / (x**3 - 2*x + 1), x) Out: 2.17082039324994*log(x - 1) + 1.34164078649988*log(x + 1/2 + sqrt(5)/2) - 1.17082039324993*log(x**3 - 2*x + 1) And looking at the code, I'd say a difference is that the Bronstein algorithm is more rigorous and general in how it generates its ansatz. But actually one of the reasons heurisch() is so slow is that it can generate ansatz that are huge (especially when it's given an integrand that doesn't have an answer to begin with). Employing some heuristics like the ones used here in heurisch could help it out. Actually it wouldn't be much work to generalize this to something that gives an exact answer at least some of the time. For example, you could use nsimplify() to guess at exact values for numeric coefficients. As long as diff(answer) - integrand symbolically simplifies to 0 you know you have a correct answer. Aaron Meurer > > -- > Oscar > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxRyJ3FUZ1pN6GACMoHZBYGbUJAavKq5Y1RW5__1nFAT8w%40mail.gmail.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6LxbG%2BZ_%2B9Q6jChaw7eQHm%2B%2BkGsbC47QyTbgN4i1wMrzw%40mail.gmail.com.
Re: [sympy] hyint: hybrid (symbolic-numeric) integration
On Tue, 29 Aug 2023 at 07:09, Shahriar Iravanian wrote: > > Hi All, > Hi Shahriar, > I have uploaded a new package, hyint, to github and PyPi. It is a hybrid > (symbolic-numeric) integration package on top of SymPy and numpy/scipy. I > would appreciate it if it is added to the list of projects using SymPy. > > You can find it at https://github.com/siravan/hyint or install it as 'pip > install hyint'. > > hyint uses an ansatz generation algorithm similar to the Risch-Bronstein poor > man's integrator combined with a sparse regression algorithm > adopted from the Sparse identification of nonlinear dynamics (SINDy) to solve > indefinite integration problems to univariate expressions. It can solve a > large subset of standard elementary integrals despite a very small size (a > few hundred lines of code). > > I'm one of the principal contributors to SymbolicNumericIntegartion.jl > (https://github.com/SciML/SymbolicNumericIntegration.jl), which is a Julia > package for symbolic-numeric integration and is the basis of hyint. This sounds excellent. Yes, you can add it to the list of projects using SymPy using a pull request, I think to the website repo. How exactly is it different from Bronstein's poor man's integrator? SymPy has an integration algorithm called heurisch which is based on the poor man's integrator but uses exact rather than approximate solutions to the linear equations. Is exact vs approximate the main distinction here between what hyint does and what heurisch does? -- Oscar -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHVvXxRyJ3FUZ1pN6GACMoHZBYGbUJAavKq5Y1RW5__1nFAT8w%40mail.gmail.com.
[sympy] hyint: hybrid (symbolic-numeric) integration
Hi All, I have uploaded a new package, hyint, to github and PyPi. It is a hybrid (symbolic-numeric) integration package on top of SymPy and numpy/scipy. I would appreciate it if it is added to the list of projects using SymPy. You can find it at https://github.com/siravan/hyint or install it as 'pip install hyint'. hyint uses an ansatz generation algorithm similar to the Risch-Bronstein poor man's integrator combined with a sparse regression algorithm adopted from the Sparse identification of nonlinear dynamics (SINDy) to solve indefinite integration problems to univariate expressions. It can solve a large subset of standard elementary integrals despite a very small size (a few hundred lines of code). I'm one of the principal contributors to SymbolicNumericIntegartion.jl (https://github.com/SciML/SymbolicNumericIntegration.jl), which is a Julia package for symbolic-numeric integration and is the basis of hyint. Thanks, Shahriar Iravanian -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/19d5e265-ddfb-4c04-9b07-4c96f4041f4cn%40googlegroups.com.
